Using Spatial Considerations in the Analysis of Experiments

Abstract

Classical experimental design is based on the three concepts of randomization, blocking, and replication. Randomization endeavors to neutralize the effects of (spatial) correlation and yields valid tests for the hypothesis of equal treatment effects. More recently, attempts have been made to use the spatial location of treatments to improve the efficiencies of estimators of treatment contrasts. In this article, we show that a simple, flexible spatial-modeling approach to the analysis of industrial experiments (e.g., wafer fabrication) can yield more efficient estimators of the treatment contrasts than the classical approach. We base the analysis on empirical generalized least squares estimation, in which the spatial-dependence parameters are estimated from resistantly detrended response data.